1. Field of the Invention
The present invention relates to a semiconductor device simulation method, and more particularly to an accurate and high-precision semiconductor device simulation method that is directed toward organic thin film transistors, a semiconductor device and fabrication method thereof, and a circuit board, electro-optical apparatus and electronic apparatus.
2. Description of the Related Art
Semiconductor device simulation involves predicting the characteristics of semiconductor devices from the structure and material properties, and so forth, of semiconductor devices or analyzing the operation of such devices. Objects of this simulation are an improvement in development efficiency by means of a decrease in the number of manufacturing experiments, the implementation of the optimum design by means of a comparison of a multiplicity of characteristics, and the proposal of development guidelines through estimation of the characteristics of transitional structures and material properties. Currently, semiconductor device simulation, which is directed toward crystal semiconductor devices, amorphous thin film transistors, and polycrystalline silicon thin film transistors, and the like, is an essential tool for research and development (Yukiharu Uraoka, 2001 FPD Technology Encyclopedia (Electronic Journal, Tokyo, 2000) 124, Yoshihisa Ino, 2001 FPD Technology Encyclopedia (Electronic Journal, Tokyo, 2000) 127, M. Kimura, Dissertation for Ph. D. (Tokyo University of Agriculture and Technology, Koganei, 2001)).
Conventional semiconductor device simulation methods include the following (S. Selberherr, Analysis and Simulation of Semiconductor Devices (Springer-Verlag, Vienna, 1984), Kenji Taniguchi, Latest processes, device simulation technologies (Realize Inc., Tokyo, 1990), Kazutaka Tomisawa, Semiconductor device simulation (Corona Publishing Co., Tokyo, 1996), Atlas User's Manual, Device Simulation Software (Silvaco International, Santa Clara, 2000)). First of all, a semiconductor device with a two-dimensional structure or three-dimensional structure, that is, semiconductors, insulators, electrodes, and peripheral spaces thereof, and so forth, of a two-dimensional structure or three-dimensional structure, are divided into meshes. Next, physical equations such as a potential equation and a carrier transport equation are established and solved for the meshes. A Poisson equation, which is a potential equation, and electron and positive-hole carrier continuity equations constituting carrier transport equations are as follows:
Poisson equation:Δψ=−ρ/∈    ψ: potential    ρ: charge volume density    ∈: permittivity
Electron carrier continuity equation:−nn∇·(μnE)−∇·(Dn∇nn)−G=0    nn: electron carrier density    μn: electron mobility    E: electric field    Dn: electron diffusion coefficient    G: carrier generation/annihilation rate
Positive-hole carrier continuity equation−np∇·(μpE)−∇·(Dp∇np)−G=0    np: positive hole carrier density    μp: positive hole mobility    E: electric field    Dp: positive hole diffusion coefficient    G: carrier generation/annihilation rate.The Finite Element Method, and difference methods, and so on, are employed as methods for establishing the equations. Further, a variety of matrix resolving methods may be used as methods for solving the equations. These equations are iterated and solved so as to converge, and, finally, the capacitance-voltage characteristics, and the transistor characteristics, and so forth are calculated in addition to the potential, carrier density, carrier flow density, and so forth.
In the above carrier continuity equations, the first term is the drift current resulting from the electric field, and the second term is the diffusion current caused by the carrier density gradient. As far as the electron and positive-hole carrier continuity equations are concerned, in cases where the physicality of the semiconductor is isotropic, the equations are arranged with the drift current and diffusion current taken together, and may be rewritten as follows:
Electron carrier continuity equation:∇·(−nnμnE−Dn∇nn)−G=0
Positive hole carrier continuity equation:∇·(−npμpE−Dp∇np)−G=0As far as the mobility expressed by the drift current equation and the diffusion coefficient expressed by the diffusion current equation are concerned, in cases where the semiconductor physicality is isotropic, the following Einstein relation is established (R. P. Feynman, The Feynman Lectures on Physics (Addison-Wesley, Massachusetts, 1965), S. M. Sze, Physics of Semiconductor Devices, 2nd ed. (John Wiley and Sons, New York, 1981)).
Einstein's relation:Dn/μn=Dp/μp=kT/q
Using Einstein's relation, the electron and positive-hole carrier continuity equations may be rewritten as follows:
Electron carrier continuity equation:μn∇·(−nnE−kT∇nn/q)−G=0
Positive hole carrier continuity equation:μp∇·(−npE−kT∇np/q)−G=0
Conventional semiconductor device simulation methods employ the electron and positive-hole carrier continuity equations detailed above.
Recently, as means for implementing lightweight, thin-type, flexible displays typified by liquid crystal displays, electroluminescence displays, and electrophoresis displays, and the like, or lightweight, thin-type, flexible sensors typified by scanners and X-ray detectors and so forth, organic thin film transistors have been the subject of active research and development (N. C. Greenham and R. H. Friend, Solid State Phys. 49, G. Horowitz, J. Appl. Phys. 70 (1991) 469, K. Waragai, Synth. Met. 55–57 (1993) 4053, L. Torsi, J. Appl. Phys. 78 (1995) 1088, G. Horowitz, J. Phys III France (1995) 355, A. R. Brown, Synth. Met. 88(1997) 37, G. Horowitz, Adv. Mater. 10(1998) 365, R. Tecklenburg, Adv. Mater. Opt. Electron. 8(1998) 285, F. Schauer, J. Appl. Phys. 86 (1999) 524, H. Sirringhaus, T. Kawase, R. H. Friend, T. Shimoda, Science 290 (2000) 2123, T. Kawase, R. H. Friend, T. Shimoda, Tech. Dig. Int. Electron Devices Meeting 2000, 623, T. Kawase, R. H. Friend, T. Shimoda, Dig. Society for Information Display 01, 40, Yoshikazu Kondou, IEICE Journal J84-C, (2001) 1050). As is true for crystal semiconductor devices, amorphous thin film transistors, and polycrystalline silicon thin film transistors, and the like, semiconductor device simulation is expected to be an essential tool in the research and development of organic thin film transistors.
Where semiconductor device simulation methods directed toward organic thin film transistors are concerned, one point to bear in mind is that, in organic semiconductor devices, mobility is highly dependent on field strength. In other words, in cases where an electric field is present, when the physicality of the semiconductor is not isotropic, the above-described Einstein relation is not established, and hence it is not possible to use the above-described electron and positive-hole carrier continuity equations.